I don't feel real warm and fuzzy about universal background checks, but even that is preferable to registration. Registration is the first step on the road to confiscation.
The irony is that, in the days of the Founders, we had registration. Every able-bodied adult male was a member of the militia, and the commanding officer of each militia unit obviously needed to know what arms his troop would have at its disposal. Since in those days each member of the militia supplied his own rifle and basic ammo load, that meant that the militia commander had a registration of what his men kept at home for weaponry.
If I could actually believe that my state and/or local police department wanted to know if I have an AR-15 so they'd know who to call up in the event of a zombie invasion, I would support that. Unfortunately, I don't think that's quite what they have in mind.